Class Of Distributed Delay Systems Research Articles

Approximation and control of a class of distributed delay systems

Abstract In this paper, we show that a linear system with distributed state delay can be approximated by a linear delay-free system that has the same state dimension as the original system if a so-called smallness condition holds. The smallness condition is an inequality which the maximum lag and norms of the system matrices have to satisfy. The eigenvalues of the approximate system correspond to the dominant eigenvalues of the original system with distributed delay. We provide a numerically stable, iterative algorithm to compute the state matrix of the approximate system. Furthermore, we show that, based on the proposed approximation, the stabilisation, pole placement and setpoint tracking control problems of the addressed class of distributed delay systems can be performed using methods developed for delay-free systems. Simulation results are provided to show the applicability of the proposed approximation and control design method.

Stability analysis for a class of distributed delay systems with constant coefficients by using a frequency‐sweeping approach

This study focuses on the stability property of a class of distributed delay systems with constant coefficients. More precisely, the authors will discuss deeper the stability analysis with respect to the delay parameter. The authors' approach will allow to give new insights in solving the so-called complete stability problem. There are three technical issues need to be studied: First, the detection of the critical zero roots (CZRs); second, the analysis of the asymptotic behaviour of such CZRs; third, the asymptotic behaviour analysis of the critical imaginary roots (CIRs) with respect to the infinitely many critical delays. They extended their recently-established frequency-sweeping approach, with which these technical issues can be effectively solved. Based on these results, a procedure was proposed, with which the complete stability analysis of such systems was accomplished systematically. Moreover, the procedure represents a unified approach: Most of the steps required by the complete stability problem may be fulfilled through observing the frequency-sweeping curves. Finally, some examples illustrate the effectiveness and advantages of the approach.

Robust adaptive tracking control of distributed delay systems with actuator and communication failures

This paper is concerned with the robust adaptive fault-tolerant tracking control problem for a class of distributed delay systems against faulted and perturbed actuators and communications. As all the faults on actuators and communications, network delays in control and communication channels, and perturbations in communications and exogenous disturbances are unknown, some adaptation schemes are developed to adjust controller parameters in real-time for constructing a class of distributed compensation controllers based on the delayed signals. Then, according to the information from the adaptive mechanism, the effect of each actuator and communication fault, network delay, channel perturbation and exogenous disturbance can be eliminated completely by using the proposed distributed adaptive-state feedback controllers. Furthermore, asymptotic tracking results of the distributed closed-loop systems can be achieved based on Lyapunov stability theory. An example is provided to further illustrate the effectiveness of the proposed direct adaptive design technique. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Predictive control for a class of distributed delay systems using Chebyshev polynomials

In this paper, the model predictive control (MPC) is developed for linear time-varying systems with distributed time delay in state. The Chebyshev operational matrices of product, integration and delay are utilized to transform the solution of distributed delay differential equation to the solution of algebraic equations. The Chebyshev functions are also applied to derive approximate solution of finite horizon optimal control problem involved in MPC. The proposed method is simple and computationally advantageous. Illustrative example demonstrates the validity and applicability of the technique.

Point delay methods applied to the investigation of stability for a class of distributed delay systems

The main target of this paper is to present criteria (adapted from the point delay systems) for the different kinds of stability, boundedness and existence of a stochastic attractor for a class of distributed delay differential stochastic equations. The new results are based on a technique of reduction of distributed delay to a lumped delay and Mao criteria for point delay equations.

Finite Dimensional Representation of Distributed Delay Systems

It is shown that a class of distributed delay systems can be represented by a system of ordinary differential equations with arbitrary degree of accuracy.